Three-dimensional Finite Difference Research Articles

A generalized curvilinear solver for spherical shell Rayleigh-Bénard convection

Summary A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi transformation and solves the governing equations in the latter. This feature enables the solver to account for the effects of the non-spherical shape of the convective regions of planets and stars. Apart from parallelization using MPI, implicit treatment of the viscous terms using a pipeline alternating direction implicit scheme and HYPRE multigrid accelerator for pressure correction makes the solver efficient for high-fidelity direct numerical simulations. We have performed simulations of Rayleigh-Bénard convection at two Rayleigh numbers Ra = 105 and 107 while keeping the Prandtl number fixed at unity (Pr = 1). The average radial temperature profile and the Nusselt number match very well, both qualitatively and quantitatively, with the existing literature. Closure of the turbulent kinetic energy budget, apart from the relative magnitude of the grid spacing compared to the local Kolmogorov scales, ensures sufficient spatial resolution.

A low loss silicon waveguide bend based on width and curvature variations

A simple, low loss and compact 90° SOI waveguide bend constructed by using an inner circular curve and an outer Euler-circular curve was proposed, optimal designed and fabricated. By adopting this simple structure, the width and curvature of the waveguide bend can be varied simultaneously, which can effectively suppress both the mode mismatch loss and the radiation loss. Three-dimensional finite difference time domain simulation results indicate a very low excess loss of about 0.0056 dB can be achieved for equivalent bending radius of 2 μm. By using the cut-back method, a low loss of about 0.0175 dB at 1550 nm was measured, which is less than one quarter of the traditional circular bend. In addition, the wavelength dependence for the proposed SOI waveguide bend was investigated and 0.0088 dB–0.0247 dB was measured in the wavelength range of 1480∼1580 nm.

Excavation method optimization and mechanical responses investigating of a shallow buried super large section tunnels: a case study in Zhejiang

The construction of super large section (SLS) shallow buried tunnels involves challenges related to their large span, high flat rate, and complex construction process. Selecting an appropriate excavation method is crucial for ensuring stability, controlling costs, and managing the construction timeline. This study focuses on the selection of excavation methods and the mechanical responses of SLS tunnels in different types of surrounding rock. The research is based on the Yangjiashan tunnel project in Zhejiang Province, China, which is a four-line highway tunnel with a span of 21.3 m. Three sequential excavation methods were proposed and simulated using the three-dimensional finite difference method: the “upper first and lower later” side drift (SD) method, the central diaphragm method, and the top heading and bench (HB) method. The mechanical response characteristics of tunnel construction under these methods were investigated, including rock deformation, rock pressure, and the internal forces acting on the primary support. By comparing the performance of the three construction methods in rock masses of Grades III to V, the study aimed to determine the optimal construction method for SLS tunnels considering factors such as safety, cost, and schedule. Field tests were conducted to evaluate the effectiveness of the optimized construction scheme. The results of the field monitoring indicated that the “upper first and lower later” SD method in Grade V rock mass and the HB method in Grade III to IV rock mass are feasible and cost-effective under certain conditions. The research findings provide valuable insights for the design and construction of SLS tunnels in complex conditions, serving as a reference for engineers and project managers.

Shaking Table Testing and Numerical Study on Aseismic Measures of Twin-Tube Tunnel Crossing Fault Zone with Extra-Large Section

As transportation networks continue to expand into mountainous regions with high seismic activity, ensuring the seismic safety of tunnels crossing active faults has become increasingly crucial. This study aimed to enhance our understanding of the impact of fault zones on the seismic behavior of tunnels and to provide optimized seismic design recommendations through a comprehensive experimental and numerical investigation. The focus of this research is the Xiangyangshan Highway Tunnel in China, which intersects a significant longitudinal fault. Large-scale shake table tests were performed on 1:100 scale physical models of the tunnel to analyze the seismic responses under various ground motion excitations. Detailed three-dimensional finite difference models were developed in FLAC3D and calibrated based on the shake table results. The tests indicated that strains, earth pressures, and accelerations experience localized amplification within 10–20 m of the fault interface compared to undisturbed ground sections. Common seismic mitigation measures, such as rock grouting, seismic joints, and shock absorption layers, were observed to effectively reduce the amplified seismic demands. Grouting, in particular, led to an average reduction of up to 56.3% in circumferential strain and 38.5% in earth pressure. It was concluded that 6 m thick grouted zones and 20 cm thick rubber interlayers between tunnel lining shells provide optimal structural reinforcement against the effects of fault zones. This study provides valuable insights for improving the seismic resilience of underground transportation corridors in seismically active regions.

Seismic Structure-Soil-Structure Interaction (SSSI) between piled neighboring bridges: Influence of height ratio

Abstract This paper explores the impact of height ratios on the seismic Structure-Soil-Structure Interaction (SSSI) for three adjacent bridges with varying superstructure masses (Mst = 350, 1050, 350 t) through 3D numerical simulations. A comprehensive series of numerical analyses has been conducted across different height ratios (R = 1, 1.1, 1.15, 1.2, 1.25, 1.5, 2, and 3) to assess their influence on superstructure acceleration and the internal forces within the foundation piles. The bridges under investigation are supported by groups of piles embedded in nonlinear clay. The numerical simulations were executed using fast Lagrangian analysis of continua in three dimensions (FLAC 3D), a three-dimensional finite differences modeling software. The findings revealed that variations in mass ratios significantly impact the SSSI effects on superstructure acceleration and pile internal forces. Notably, adverse effects were more pronounced for mass ratios of R = 1.1 and 1.2, leading to an increase in bending moment, shear force, and superstructure acceleration by up to 237.8%, 291.4%, and 70.33%, respectively. In contrast, a mass ratio of R = 3 resulted in a decrease in bending moment, shear force, and superstructure acceleration by up to 72%, 82.14%, and 81.13%, respectively. This implies that a careful arrangement of adjacent structures with different masses can be employed effectively to manage the (SSSI) effects.

Numerical study on stability of geosynthetic-encased stone column-supported embankments based on equivalent method

The application of geosynthetic-encased stone column-supported embankments (GESC-supported embankments) has garnered significant attention in geotechnical engineering, with limited investigations into their slope stability. In this paper, an equivalent method was proposed to establish GESC-supported embankment models through three-dimensional finite difference method (3D-FDM). Responses of factor of safety (FS) to arrangement tightness of GESCs (e.g., various column diameters, spacings, and quantities under constant area replacement ratio) and hoop effect of geosynthetic encasements (e.g., various geogrid strengths under different shear strengths of soft soil) were studied. For a given area replacement ratio, FS increased non-linearly with the increasing column quantity or the decreasing ratio of column spacing to diameter at high area replacement ratios. GESCs with smaller diameter and spacing proved to be more effective in improving slope stability, and an optimum ratio of column spacing to diameter was observed for practical use. Besides, FS increased linearly with geogrid strength at low geogrid strength levels, but an extremely lack of the shear strength of soft soils or the column quantity was unfavorable for the application of GESCs. Bending failure was the primary failure feature of GESCs under embankment loading, and the geogrid strength influenced slope stability through the bending capacity of GESCs.

Basin boundary seismic effects in Mexico City southern region

AbstractRapid changes in geotechnical and geological ground conditions lead to significant ground motion variability. This condition mainly occurs at the so-called basin edges, where there is an abrupt transition between soft highly compressible soils and stiffer materials. This problem becomes more relevant in areas where ground subsidence drastically changes the dynamic response of high plasticity clay deposits, such as those found in Mexico City, due to fundamental site period evolution with time. This paper presents site response analyses at an abrupt transition area in the southeast Mexico City region, along the edges of the Xochimilco-Chalco lakes. Considerable damage associated with three-dimensional wave propagation effects was observed in this zone during the September 2017 Puebla-Mexico earthquake. A series of three-dimensional finite difference numerical models of the basin edge were developed to evaluate ground motion variability, considering topographic effects and soil non-linearities. Good agreement between the computed response and the observed damage during the 2017 Puebla-Mexico earthquake reconnaissance was found. In addition, several normal and subduction events with a return period of 250 years were considered to evaluate the effect that frequency content, and strong ground motion duration have on the soil response variability. From the results gathered here, it was established the relevance of accounting for three-dimensional wave propagation fields to assess site effects at basin-edge zones properly and to be able to implement proper risk mitigation measurements at these zones.

Seismic response of tripod suction bucket foundation for offshore wind turbine in sands

Tripod suction bucket foundation is increasingly used to support offshore wind turbines (OWTs) due to its convenient and low-cost installation and high overturning resistance. However, the seismic response characteristics of OWTs of tripod bucket foundations in sands is not well covered in the literature. Therefore, this study investigates the response of tripod bucket foundations installed in sands and subjected to seismic loads employing advanced three-dimensional finite difference analysis. The variation of pore pressure around suction bucket is evaluated, and the failure mechanism of the tripod bucket foundation in sands is revealed. In addition, the displacement response of the tower, and the acceleration amplification effect of the OWT system are elucidated. It is found that the earthquake magnitude, and sand relative density and liquefaction greatly affect the foundation seismic behavior. The results revealed that the overall rotation of the tripod bucket foundation is primarily due to progressively increasing differential vertical settlement between the foundation sides of ‘single bucket’ and ‘double bucket’ associated with loading direction. It was also found that the sand liquefaction under strong shaking may lead to excessive rotation of the foundation that exceeds the service limit state. The findings from this study can provide guidance for the design of OWT tripod bucket foundations in sands.

Highly compact tunable hourglass-shaped graphene band-stop filter at terahertz frequencies

In this research paper, we introduce a band-stop filter based on an hourglass-shaped graphene nanoribbon topology. Employing the three-dimensional finite difference time domain (3D-FDTD) method, we conduct comprehensive numerical simulations to investigate transmission spectra and electromagnetic field distributions. Our primary objectives are to achieve high transmission efficiency, increase tunability, and ensure compact dimensions. The hourglass-shaped band-stop filter exhibits a remarkable bandwidth of 1.2 THz, a 90 % transmission efficiency in the passband, an impressive attenuation of −52.5 dB at the resonance frequency of 32.3 THz, and a compact footprint of 400×300 nm2. By manipulating the chemical potential (or bias voltage) to control the conductivity and dielectric constant of the graphene surface, we set the center frequency of the filter in the range of 28 to 36 terahertz. The remarkable combination of high transmission efficiency, high tunability, and compact design makes our proposed filter an ideal candidate for integration.

P-y Curve for Estimation Lateral Bearing Capacity of Single Bored Pile in Overconsolidated Soils Using The Three-Dimensional Finite Element Method.

The p-y curve method is widely used to predict piles’ lateral bearing capacity. It assumes independent springs with a non-linear modulus of subgrade reaction for analyzing soil resistance (p) and deflection (y). This study determined the lateral bearing capacity using the three-dimensional finite element method (FEM-3D) and finite difference method (FDM), which was later compared with the loading test results. Therefore, the pile head condition is assumed to be the free-head. To determine the lateral bearing capacity, input the lateral deflection at the pile head. In FEM-3D, the pile and lateral deflection in the pile head is modeled using cluster elements and surface-prescribed horizontal displacements, respectively. On the other hand, in FDM, pile heads and boundary conditions are modeled using displacement and moment. The results of the lateral bearing capacity using FEM-3D provide predictions that are close to the loading test, with a difference of about 4.2%. In contrast, the FDM method produced conservative results due to its reliance on semi-empirical formulas. The ultimate soil resistance (Pult) formula in FDM is more suitable for rigid-pile behavior. The prediction of lateral bearing capacity using FEM-3D provides more accurate results due to its ability to model complex soil-pile interaction. The stress history, soil-pile interaction, and more reliable constitutive models can be modeled in FEM-3D.

Study on the detection technology and response of isolated anomalous bodies in transient electromagnetic wave logging of formations

Transient electromagnetic wave logging is one of the key methods for detecting underground formations, especially for identifying anomalies near wells using higher frequencies and resolutions. In this paper, the 3D TDFD (three-dimensional time-domain finite-difference) simulation method is used to investigate the detection technique of wellbore anomalies based on the scattered field of transient electromagnetic waves and its significance in underground structure identification and localization. The research results show that isolated anomalies can be effectively characterized by extracting the scattering field response generated by block-shaped anomalies while eliminating the contribution of background media. Analyzing the measurement response caused by scatterers provides important information about the position, size, and response magnitude of the anomalies, offering an effective method for detecting and identifying wellbore anomalies. Applying this detection technique enriches the existing methods for wellbore anomaly detection, providing important theoretical and technical foundations for petroleum and solid mineral exploration, as well as the construction of underground defense engineering.

Three-Dimensional Numerical Transfer Model Using a Monotonized Z-Scheme

The aim of this work is to investigate a three-dimensional second-order monotone finite-difference scheme for the transport equation. The investigation is conducted for model three-dimensional transport equations of an incompressible medium. The properties of the three-dimensional extension of the Z-scheme with nonlinear correction are studied in this work. This study is an extension of the author’s previous works, where a nonlinear correction of one-dimensional transport equations was constructed. The proposed scheme uses “skew differences” containing values from different time layers instead of fluxes for the correction. The monotonicity of the obtained nonlinear scheme is numerically studied for a family of limiter functions for both smooth and non-smooth continuous solutions. The constructed scheme is absolutely stable but loses the monotonicity property when the Courant step is exceeded. The distinctive feature of the proposed finite-difference scheme is the minimalism of its template. The constructed numerical scheme is designed for models of plasma instabilities of various scales in the low-latitude ionospheric plasma of the Earth. One of the real problems that arise in solving such equations is the numerical modeling of strongly non-stationary medium- and small-scale processes in the low-latitude ionosphere of the Earth under conditions of the occurrence of the Rayleigh–Taylor instability and other types of instabilities, leading to the phenomenon of F‑scattering. Due to the fact that transport processes in the ionospheric plasma are controlled by the magnetic field, it is assumed that the plasma is incompressible in the direction perpendicular to the magnetic field.

Polarization-insensitive metamaterial perfect absorber in near-infrared band based on trapezoidal silver array

In this article, we presented our proposal for a metamaterial perfect absorber (MPA) operating in the near-infrared band. Our MPA comprised a trapezoidal silver layer, a substrate layer, and an intermediate alumina layer. The transmission characteristics of MPA were analyzed by the three-dimensional (3D) finite difference time domain method. The simulation results were analyzed by equivalent circuit theory. The results show that the MPA achieved 100% absorption of transverse magnetic (TM) polarization and transverse electric (TE) polarization with resonance wavelength = 1492.5 nm. By varying the length of the bottom side of the trapezoid, the MPA’s resonance wavelength could be effectively tuned, and the absorption was maintained at above 99%. With the incidence angle of 0°–55°, the absorption remains above 90% at TE polarization and above 80% at 55°–70°. The absorption at the TM polarization remains above 99% when the incident angle is 0°–70°. A wide angle of incidence and good absorption were achieved. The sensitivity (S) and figure of merit were 228 nm/refractive index unit and 1378 RIU−1, respectively. The proposed absorber with excellent absorption in the range of infrared spectra has a promising application potential in fields such as energy harvesting and infrared sensors.

Three-dimensional lattice Boltzmann and finite difference methods for the simulation of ultrasound and thermal convection in a microcavity

This article presents a three-dimensional numerical analysis of the phenomena of ultrasound propagation in air, thermal convection, and their interaction. The simulations are carried out using a hybrid numerical approach based on the lattice Boltzmann and the finite difference techniques. For validation purposes, our numerical model is verified in the case of the study of ultrasound propagation in the air without the presence of thermal convection. This is performed by comparing the numerically calculated acoustic pressure with the analytical results. After this verification, the focus is on the examination of the heat transfer improvement by the ultrasound emitted by the vibration of a circular piston. This acoustic source is mounted in the center of the left cold surface of a microcavity, which is differentially heated and filled with air. The obtained numerical results indicate that the heat transfer is significantly improved by using 10 MHz ultrasound.

Settlement Behavior of Composite Foundation with Deep Mixed Piles Supporting Highway Subgrades in Water-Rich Flood Plains

The settlement behavior of composite foundations plays an important role in the serviceability and stability of the subgrade or other infrastructures supporting the foundation. However, in water-rich flood plains, due to the complexity of the soft soil properties, the settlement behavior has not been well understood. The objective of this study is to investigate the effects of various key factors on the settlement behavior of composite foundations with deep mixed piles supporting highway subgrade in water-rich flood plains. The investigated subgrade is in operation, and the vehicle load is taken into account. The G347AH Project is considered in this study. Several typical models for predicting composite foundation settlements are discussed. By performing three-dimensional finite difference analysis, a comparison is made between the settlement behavior of the natural foundation and the composite foundation with deep mixed piles. Based on the single factor sensitivity analysis and the multi-factor orthogonal experimental design, the effects of pile length, pile diameter, pile spacing, pile elasticity modulus, cushion elasticity modulus, and cushion thickness on the composite foundation settlement are captured. It is found that among these factors, the degree of influence of pile length is superior. The composite foundation settlements predicted by the models agree well with the field-monitoring data, with the error being about 8.42% and 6.38%, respectively, at two monitoring sections. The research conducted in this paper can effectively reduce the probability of various settlement-related disasters occurring on highway subgrades in water-rich flood plains. Moreover, the research has important theoretical guidance for design optimization in terms of settlement control of highway subgrades in soft soil areas.

Theoretical study of Ag and Au triple core-shell spherical plasmonic nanoparticles in ultra-thin film perovskite solar cells.

This work demonstrates the enhancement of the power conversion efficiency of thin film organic-inorganic halide perovskites solar cells by embedding triple-core-shell spherical plasmonic nanoparticles into the absorber layer. A dielectric-metal-dielectric nanoparticle can be substituted for embedded metallic nanoparticles in the absorbing layer to modify their chemical and thermal stability. By solving Maxwell's equations with the three-dimensional finite difference time domain method, the proposed high-efficiency perovskite solar cell has been optically simulated. Additionally, the electrical parameters have been determined through numerical simulations of coupled Poisson and continuity equations. Based on electro-optical simulation results, the short-circuit current density of the proposed perovskite solar cell with triple core-shell nanoparticles consisting of dielectric-gold-dielectric and dielectric-silver-dielectric nanoparticles has been enhanced by approximately 25% and 29%, respectively, as compared to a perovskite solar cell without nanoparticles. By contrast, for pure gold and silver nanoparticles, the generated short-circuit current density increased by nearly 9% and 12%, respectively. Furthermore, in the optimal case of the perovskite solar cell the open-circuit voltage, the short-circuit current density, the fill factor, and the power conversion efficiency have been achieved at 1.06 V, 25 mAcm-2, 0.872, and 23.00%, respectively. Last but not least, lead toxicity has been reduced due to the ultra-thin perovskite absorber layer, and this study provides a detailed roadmap for the use of low-cost triple core-shell nanoparticles for efficient ultra-thin-film perovskite solar cells.

Mechanical Properties of Sheet Pile Cofferdam during Adjacent Open Cut Tunnel Construction near Lake Bottom

In water-related projects, the application of steel sheet pile cofferdams is becoming more and more widespread, and the influence of tunnel construction on the mechanical properties of adjacent cofferdams is important. In this study, the object of research was the mechanical properties of large-span steel sheet pile cofferdams. The open-cut tunnel project was located in Suzhou Yinshan Lake, China. According to the actual construction steps of the tunnel foundation pit, assuming that the soil was a small strain hardening soil model, combined with on-site monitoring data, a three-dimensional elastoplastic finite difference model was established. The results show that during tunnel construction, the maximum settlement of the cofferdam appeared at 0.27~0.53 m on the side of the foundation pit; the maximum horizontal displacement of the steel sheet pile occurred at the pile bottom of foundation pit side, and the seepage gradually increased during construction, eventually resulting in water gushing at the bottom of the foundation pit. After the completion of tunnel construction, the settlement value of the cofferdam presented a pattern that first increased and then decreased from the side of the foundation pit to the side of the adjacent lakeside; the steel cofferdam tilted toward the side of the foundation pit, with a maximum inclination angle of 3.37°. It should be pointed out that as the construction progressed, the axial force of the tie rods in the steel cofferdam changed from a U-shaped distribution to a V-shaped distribution. This study could provide a reference for the impact of tunnel foundation pit construction on adjacent steel cofferdam and could also provide a reference for the safety research of open-cut tunnel construction.

Face stability of shallowly buried large-section EPB box jacking crossing the Beijing-Hangzhou Grand Canal

The mechanical response of conditioned soil in an earth chamber is crucial for maintaining the face stability of earth pressure balance (EPB) box jacking. This study presents the project of a shallowly buried large-section box jacking crossing the Beijing-Hangzhou Grand Canal in Suzhou, China. The characteristics of tunneling parameters, such as the earth chamber pressure pe, total jacking force Pf and frictional force Ffric, were revealed by field measurements. A refined three-dimensional finite difference model was developed using the fluid–solid coupling analysis mode to evaluate the tunnel face stability, in which the geometric configurations of box jacking machine and the contact interfaces between different components were considered explicitly. In addition, the differences between driving and stoppage of box jacking machine were also considered. Upon the successful calibration of the numerical model, the transfer mechanism and the face support efficacy of conditioned soil are evaluated. In the end, a parametric study was conducted to discuss the influences of conditioned soil permeability, shear strength and thickness. The results indicate that the permeability of conditioned soil has no significant influence on its mechanical response, and a larger shear strength can obviously enhance the stress level at the lower part of the earth chamber. In addition, a larger thickness of conditioned soil can reduce its transfer coefficient and the fluctuation of earth chamber pressure.

3D numerical modeling of a rigid inclusion reinforced railway embankment under cyclic loading

Rigid inclusion reinforcements of embankments are increasingly used in traffic route engineering to ensure the long-term system sustainability and to enhance the soft subsoils load-bearing capacity under static and cyclic loading conditions in an economical and practical way. This paper presents a three-dimensional numerical finite difference model to assess the performance of a rigid inclusion reinforced railway embankment subjected to cyclic loading. A slice model of the railway embankment is considered based on full-scale physical tests. The advanced elasto-plastic SANISAND constitutive model is considered for the granular layer in the rigid inclusion reinforced railway embankment. The responses of the system under cyclic loading are outlined concerning settlements, stress distribution and axial–flexural response of the rigid inclusions.

Modeling of heating and cooling behaviors of laminated glass facades exposed to fire with three-dimensional flexibilities

To develop a precise and efficient computer model for predicting the heating and cooling behaviors of laminated glass facades exposed to fire, there is an urgent need to reduce the huge computational requirements associated with simulating heat transfer in layered structures that feature a down-flowing water film. We overcome this challenge by proposing an efficient three-dimensional finite difference method (3DFDM) which has high numerical stability when solving heat transfer equations with water film and air convection. To capture the moving particles of the water film, we developed a unique computational algorithm for particle labeling, which has two significant advantages: (1) it eliminates the time-consuming process of searching for neighboring particles in conventional meshfree methods, and (2) it ensures that every main particle interacts only with limited neighboring particles without utilizing any weights, thus significantly reducing the computational effort. We validated our 3DFDM through experiments in heating and cooling scenarios and compared its thermal results with those obtained from commercial packages to demonstrate its high efficiency and accuracy. Furthermore, we examined the feasibility of our model in evaluating the effects of thickness of the interlayer and water film release time on the cooling behavior of laminated glass during a fire.